# kindly explain me solution of integration

• Sep 17th 2009, 05:02 AM
moonnightingale
kindly explain me solution of integration
Kindly explain me this solution in detail
I have attached the three questions. I will be highly greatful if anyone of you explain me these solutions in Detail. Thaks a lot

Attachment 12939

Attachment 12940
• Sep 17th 2009, 06:29 AM
CaptainBlack
Quote:

Originally Posted by moonnightingale
Kindly explain me this solution in detail
I have attached the three questions. I will be highly greatful if anyone of you explain me these solutions in Detail. Thaks a lot

Attachment 12939

$\displaystyle \cos^2(2 \pi f_0 t) = (\cos(4 \pi f_0 t)+1)/2$

then as $\displaystyle \cos$ is symetrical in all sorts of ways the right hand side will integrate up to half the area eonclosed in the rectangle enclosing the curve, which has height $\displaystyle 1$ and length $\displaystyle T_0$.

(Draw a picture of the curve, it will then be obvious)

CB
• Sep 17th 2009, 06:32 AM
CaptainBlack
Quote:

Originally Posted by moonnightingale
Kindly explain me this solution in detail
I have attached the three questions. I will be highly greatful if anyone of you explain me these solutions in Detail. Thaks a lot

Attachment 12939

Attachment 12940

(b) is a direct consequence of (a) (multiply the integral in (a) by $\displaystyle T_0$ to get that in (b)

CB